Question

The floor of a building consists of around 3000 tiles which are rhombus shaped and each of its diagonals are 45cm and 25 cm in length. Find the total cost of flooring if each tile costs Rs 20 Per sqm​

Answer 1

Answer:

Rs.3375

Explanation:

Given,

The floor of a building consists of 3000 rhombus shaped tiles of diagonals 45cm and 25cm.

Find the total cost of flooring each tiles if the rate is Rs.20/m²

Total cost of flooring is given by,

→ Area acquired for flooring × rate of flooring.

Let's calculate the area acquired,

→ Area of one tile × 3000

Since the tile is rhombus shaped,

→ Area of one tile = ½*p*q

Where,

• p is one diagonal.
• q is another diagonal.

So,

→ ½*(45)*(25)

→ ½*(1125)

→ 562.5cm²

Total area acquired,

→ 562.5 × 3,000

→ 1687500cm²

On converting into m²

→ 1687500 ÷ 10000 [Since, 1m² = 10000cm²]

→ 168.75m²

Now, total cost of flooring is :-

→ 168.75 × 20

→ 3375

∴ Required answer: Rs.3,375.

__________________________

$\:$

Answer 2

Answer:

Given :-

• The floor of a building consists of around 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 25 cm in length.

To Find :-

• What is the total cost of flooring if each tile costs Rs 20 per m².

Formula Used :-

$\clubsuit$ Area Of Rhombus Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Rhombus)} =\: \dfrac{d_1 \times d_2}{2}}}}\: \: \: \bigstar$

where,

• d₁ = First Diagonal of Rhombus
• d₂ = Other Diagonal of Rhombus

Solution :-

First, we have to find the area of each tiles :

Given :

• Diagonal (d₁) = 45 cm
• Diagonal (d₂) = 25 cm

According to the question by using the formula we get,

$\implies \bf Area_{(Rhombus)} =\: \dfrac{d_1 \times d_2}{2}$

$\implies \sf Area_{(Rhombus)} =\: \dfrac{45 \times 25}{2}$

$\implies \sf Area_{(Rhombus)} =\: \dfrac{1125}{2}$

$\implies \sf\bold{\blue{Area_{(Rhombus)} =\: 562.5\: cm^2}}$

Hence, the area of each tiles is 562.5 cm² .

Now, we have to find the total area of the floor :

Given :

• Number of tiles = 3000 tiles
• Area of each tiles = 562.5 cm²

According to the question by using the formula we get,

$\footnotesize \leadsto \bf Total\: Area of\: Floor =\: Number\: of\: tiles \times Area\: of\: each\: tiles$

$\leadsto \sf Total\: Area\: of\: Floor =\: 3000 \times 562.5$

$\leadsto \sf\bold{\green{Total\: Area\: of\: Floor =\: 1687500\: cm^2}}$

Now, we have to convert the total area of floor cm² into m² :

$\mapsto \bf Total\: Area\: of\: Floor =\: 1687500\: cm^2$

$\mapsto \sf Total\: Area\: of\: Floor =\: \dfrac{1687500}{10000}\: m^2\: \: \bigg\lgroup \sf\bold{\pink{1\: cm^2 =\: \dfrac{1}{10000}\: m^2}}\bigg\rgroup$

$\mapsto \sf\bold{\purple{Total\: Area\: of\: Floor =\: 168.75\: m^2}}$

Now, we have to find the total cost of flooring :

Given :

• Cost of flooring each tiles per m² = Rs 20 per m²
• Total Area of Floor = 168.75 m²

According to the question by using the formula we get,

$\footnotesize \dashrightarrow \bf Total\: Cost\: of\: Flooring =\: Total\: Area\: of\: Floor \times Cost\: of\: Flooring$

$\dashrightarrow \sf Total\: Cost\: of\: Flooring =\: 168.75 \times 20$

$\dashrightarrow \sf\bold{\red{Total\: Cost\: of\: Flooring =\: Rs\: 3375}}$

$\therefore$ The total cost of flooring is Rs 3375 .

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